Speaking of pocket watches, does anyone know what to call a watch with a black face and possessing no cover (alternatively a transparent cover). Is that a military watch?
It could be called miltary styled, as that was a style that was used in the military. Typically, military watches will allways be marked as such, usually with (in the UK, the US is different) with the "broad arrow' (the "pheon"), and G.S.T.P 9General Service TimePiece) markings, and serial number.
examples
Swiss Recta, 15 jewel, styled as you mentioned.. Note the the markings on the back. UK issue.

Bravia, again, Swiss, 15 jewel, but white dialed -

Note that under the broad arrow mark, is stamped an "S" - this indicates the watch was "Sold out of service", in this case, to Bravington's, a London jeweller, who sold quite a few military pocket watches after the war.

US military pocket watches typically had a mil-spec number, serial number and issue date on the back..
Cheers
Harold